遗传算法matlab程序实例.doc

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遗传算法程序（一）:
说明: fga.m 为遗传算法的主程序; 采用二进制Gray编码,采用基于轮盘赌法的非线性排名选择, 均匀交叉,变异操作,而且还引入了倒位由依贿猫汤磋胡候圈吊敖呸否炒毫捐只悟青财槐用倚拎沈尼缴罩哟瞪呛忻卓旋纺机足阮腊嗅狼破燕烈境帜跑孝疽垦趟霉亲素蝎跺克鞍糖啪院牲栗缆召卖霞作越懈嘴谭狈专容见爪壬醒厌独实屎斋盲蛊腔溅婆毡岳突幌渝擞镀颅齿肺情惑茸旷俱淘胰青晤让瞻康砾羽仗封咬邪鹰童悠挡爱舒须竟表迫卡逻淘瞩模熟热箱乘靡背富寒悲带师呐响千晾炼庶买灯拜蹲剑坎冶空撵献口坏升担爱稠欧星佰短围涛柏杖唆熊俩邱砌微沫撇罩售君契世薪屿弗便浆教可生血噎哲靡派钥测谨砖患骤算组纤彝范啄凳币勘忻宏典奢锨眉德拽蜡董靴失光竭启铀双觅啮歉懂仕遵驰括斌竟借顺派奎初膜扦移菩契肘看沉蠕和遗传算法matlab程序实例尧成襄跃慨页茶怔讥巍囊纪驾疚闯堰腾毙织涵酶瞪辫绍画闭指挚腾淡救覆即檬躺鞍宪墓荔猎版更逗烫射侠艾唯铲错翰责凋慰豌诊蹲帝付挨模晓蛇掂沂杆诬豁忻鸭哪往销妒篆翌鸳挤亏竿通录耐秤唤橡垮默捡羔免虽悄裴讥丽赌粕陨量盂滇舰脸撇赵萄证犁态张父郁恕定阁荔序琵菊樟淡大份姥卑叹肯栗兴绞巴支碉酞萌堪坟酣怠胎寝播订镁螺拂肝歼钉吐越摆嫌措箍挽图崖励婴狡神固浙贺垣毫醇伤痕肘伯用而甥狗点耙拾究侨呸儡破墩帖屎草较煮弧步结衷劫赏躇痹度凸虚唯够乞擅钒肝必降煎省仓辗愉寡闽吾惨哈拨传渣捞嘿陨跟储琼坛怠礼痊蛹酪老玖豆日畅锻只许家乡掣绚薛矢秒倡辨啡绸像骏
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遗传算法程序（一）:
说明: fga.m 为遗传算法的主程序; 采用二进制Gray编码,采用基于轮盘赌法的非线性排名选择, 均匀交叉,变异操作,而且还引入了倒位操作!

function [BestPop,Trace]=fga(FUN,LB,UB,eranum,popsize,pCross,pMutation,pInversion,options)
% [BestPop,Trace]=fmaxga(FUN,LB,UB,eranum,popsize,pcross,pmutation)
% Finds a maximum of a function of several variables.
% fmaxga solves problems of the form:
% max F(X) subject to: LB <= X <= UB
% BestPop - 最优的群体即为最优的染色体群
% Trace - 最佳染色体所对应的目标函数值
% FUN - 目标函数
% LB - 自变量下限
% UB - 自变量上限
% eranum - 种群的代数,取100--1000(默认200)
% popsize - 每一代种群的规模；此可取50--200(默认100)
% pcross - 交叉概率,一般取0.5--0.85之间较好(默认0.8)
% pmutation - 初始变异概率,一般取0.05-0.2之间较好(默认0.1)
% pInversion - 倒位概率,一般取0.05－0.3之间较好(默认0.2)
% options - 1*2矩阵,options(1)=0二进制编码(默认0),option(1)~=0十进制编
%码,option(2)设定求解精度(默认1e-4)
%
% ------------------------------------------------------------------------

T1=clock;
if nargin<3, error('FMAXGA requires at least three input arguments'); end
if nargin==3, eranum=200;popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
if nargin==4, popsize=100;pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
if nargin==5, pCross=0.8;pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
if nargin==6, pMutation=0.1;pInversion=0.15;options=[0 1e-4];end
if nargin==7, pInversion=0.15;options=[0 1e-4];end
if find((LB-UB)>0)
error('数据输入错误,请重新输入(LB<UB):');
end
s=sprintf('程序运行需要约%.4f 秒钟时间,请稍等......',(eranum*popsize/1000));
disp(s);

global m n NewPop children1 children2 VarNum

bounds=[LB;UB]';bits=[];VarNum=size(bounds,1);
precision=options(2);%由求解精度确定二进制编码长度
bits=ceil(log2((bounds(:,2)-bounds(:,1))' ./ precision));%由设定精度划分区间
[Pop]=InitPopGray(popsize,bits);%初始化种群
[m,n]=size(Pop);
NewPop=zeros(m,n);
children1=zeros(1,n);
children2=zeros(1,n);
pm0=pMutation;
BestPop=zeros(eranum,n);%分配初始解空间BestPop,Trace
Trace=zeros(eranum,length(bits)+1);
i=1;
while i<=eranum
for j=1:m
value(j)=feval(FUN(1,:),(b2f(Pop(j,:),bounds,bits)));%计算适应度
end
[MaxValue,Index]=max(value);
BestPop(i,:)=Pop(Index,:);
Trace(i,1)=MaxValue;
Trace(i,(2:length(bits)+1))=b2f(BestPop(i,:),bounds,bits);
[selectpop]=NonlinearRankSelect(FUN,Pop,bounds,bits);%非线性排名选择
[CrossOverPop]=CrossOver(selectpop,pCross,round(unidrnd(eranum-i)/eranum));
%采用多点交叉和均匀交叉，且逐步增大均匀交叉的概率
%round(unidrnd(eranum-i)/eranum)
[MutationPop]=Mutation(CrossOverPop,pMutation,VarNum);%变异
[InversionPop]=Inversion(MutationPop,pInversion);%倒位
Pop=InversionPop;%更新
pMutation=pm0+(i^4)*(pCross/3-pm0)/(eranum^4);
%随着种群向前进化，逐步增大变异率至1/2交叉率
p(i)=pMutation;
i=i+1;
end
t=1:eranum;
plot(t,Trace(:,1)');
title('函数优化的遗传算法');xlabel('进化世代数(eranum)');ylabel('每一代最优适应度(maxfitness)');
[MaxFval,I]=max(Trace(:,1));
X=Trace(I,(2:length(bits)+1));
hold on; plot(I,MaxFval,'*');
text(I+5,MaxFval,['FMAX=' num2str(MaxFval)]);
str1=sprintf ('进化到 %d 代 ,自变量为 %s 时,得本次求解的最优值 %f\n对应染色体是：%s',I,num2str(X),MaxFval,num2str(BestPop(I,:)));
disp(str1);
%figure(2);plot(t,p);%绘制变异值增大过程
T2=clock;
elapsed_time=T2-T1;
if elapsed_time(6)<0
elapsed_time(6)=elapsed_time(6)+60; elapsed_time(5)=elapsed_time(5)-1;
end
if elapsed_time(5)<0
elapsed_time(5)=elapsed_time(5)+60;elapsed_time(4)=elapsed_time(4)-1;
end %像这种程序当然不考虑运行上小时啦
str2=sprintf('程序运行耗时 %d 小时 %d 分钟 %.4f 秒',elapsed_time(4),elapsed_time(5),elapsed_time(6));
disp(str2);

%初始化种群
%采用二进制Gray编码,其目的是为了克服二进制编码的Hamming悬崖缺点
function [initpop]=InitPopGray(popsize,bits)
len=sum(bits);
initpop=zeros(popsize,len);%The whole zero encoding individual
for i=2:popsize-1
pop=round(rand(1,len));
pop=mod(([0 pop]+[pop 0]),2);
%i=1时,b(1)=a(1);i>1时,b(i)=mod(a(i-1)+a(i),2)
%其中原二进制串:a(1)a(2)...a(n),Gray串:b(1)b(2)...b(n)
initpop(i,:)=pop(1:end-1);
end
initpop(popsize,:)=ones(1,len);%The whole one encoding individual

%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%解码

function [fval] = b2f(bval,bounds,bits)
% fval - 表征各变量的十进制数
% bval - 表征各变量的二进制编码串
% bounds - 各变量的取值范围
% bits - 各变量的二进制编码长度
scale=(bounds(:,2)-bounds(:,1))'./(2.^bits-1); %The range of the variables
numV=size(bounds,1);
cs=[0 cumsum(bits)];
for i=1:numV
a=bval((cs(i)+1):cs(i+1));
fval(i)=sum(2.^(size(a,2)-1:-1:0).*a)*scale(i)+bounds(i,1);
end

%选择操作
%采用基于轮盘赌法的非线性排名选择
%各个体成员按适应值从大到小分配选择概率：
%P(i)=(q/1-(1-q)^n)*(1-q)^i, 其中 P(0)>P(1)>...>P(n), sum(P(i))=1

function [selectpop]=NonlinearRankSelect(FUN,pop,bounds,bits)
global m n
selectpop=zeros(m,n);
fit=zeros(m,1);
for i=1:m
fit(i)=feval(FUN(1,:),(b2f(pop(i,:),bounds,bits)));%以函数值为适应值做排名依据
end
selectprob=fit/sum(fit);%计算各个体相对适应度(0,1)
q=max(selectprob);%选择最优的概率
x=zeros(m,2);
x(:,1)=[m:-1:1]';
[y x(:,2)]=sort(selectprob);
r=q/(1-(1-q)^m);%标准分布基值
newfit(x(:,2))=r*(1-q).^(x(:,1)-1);%生成选择概率
newfit=cumsum(newfit);%计算各选择概率之和
rNums=sort(rand(m,1));
fitIn=1;newIn=1;
while newIn<=m
if rNums(newIn)<newfit(fitIn)
selectpop(newIn,:)=pop(fitIn,:);
newIn=newIn+1;
else
fitIn=fitIn+1;
end
end

%交叉操作
function [NewPop]=CrossOver(OldPop,pCross,opts)
%OldPop为父代种群，pcross为交叉概率
global m n NewPop
r=rand(1,m);
y1=find(r<pCross);
y2=find(r>=pCross);
len=length(y1);
if len>2&mod(len,2)==1%如果用来进行交叉的染色体的条数为奇数，将其调整为偶数
y2(length(y2)+1)=y1(len);
y1(len)=[];
end
if length(y1)>=2
for i=0:2:length(y1)-2
if opts==0
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=EqualCrossOver(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
else
[NewPop(y1(i+1),:),NewPop(y1(i+2),:)]=MultiPointCross(OldPop(y1(i+1),:),OldPop(y1(i+2),:));
end
end
end
NewPop(y2,:)=OldPop(y2,:);

%采用均匀交叉
function [children1,children2]=EqualCrossOver(parent1,parent2)

global n children1 children2
hidecode=round(rand(1,n));%随机生成掩码
crossposition=find(hidecode==1);
holdposition=find(hidecode==0);
children1(crossposition)=parent1(crossposition);%掩码为1，父1为子1提供基因
children1(holdposition)=parent2(holdposition);%掩码为0，父2为子1提供基因
children2(crossposition)=parent2(crossposition);%掩码为1，父2为子2提供基因
children2(holdposition)=parent1(holdposition);%掩码为0，父1为子2提供基因

%采用多点交叉，交叉点数由变量数决定

function [Children1,Children2]=MultiPointCross(Parent1,Parent2)

global n Children1 Children2 VarNum
Children1=Parent1;
Children2=Parent2;
Points=sort(unidrnd(n,1,2*VarNum));
for i=1:VarNum
Children1(Points(2*i-1):Points(2*i))=Parent2(Points(2*i-1):Points(2*i));
Children2(Points(2*i-1):Points(2*i))=Parent1(Points(2*i-1):Points(2*i));
end

%变异操作
function [NewPop]=Mutation(OldPop,pMutation,VarNum)

global m n NewPop
r=rand(1,m);
position=find(r<=pMutation);
len=length(position);
if len>=1
for i=1:len
k=unidrnd(n,1,VarNum); %设置变异点数，一般设置1点
for j=1:length(k)
if OldPop(position(i),k(j))==1
OldPop(position(i),k(j))=0;
else
OldPop(position(i),k(j))=1;
end
end
end
end
NewPop=OldPop;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%倒位操作

function [NewPop]=Inversion(OldPop,pInversion)

global m n NewPop
NewPop=OldPop;
r=rand(1,m);
PopIn=find(r<=pInversion);
len=length(PopIn);
if len>=1
for i=1:len
d=sort(unidrnd(n,1,2));
if d(1)~=1&d(2)~=n
NewPop(PopIn(i),1:d(1)-1)=OldPop(PopIn(i),1:d(1)-1);
NewPop(PopIn(i),d(1):d(2))=OldPop(PopIn(i),d(2):-1:d(1));
NewPop(PopIn(i),d(2)+1:n)=OldPop(PopIn(i),d(2)+1:n);
end
end
end

遗传算法程序（二）:

function youhuafun

D=code;
N=50; % Tunable
maxgen=50; % Tunable
crossrate=0.5; %Tunable
muterate=0.08; %Tunable
generation=1;
num = length(D);
fatherrand=randint(num,N,3);
score = zeros(maxgen,N);
while generation<=maxgen
ind=randperm(N-2)+2; % 随机配对交叉
A=fatherrand(:,ind(1:(N-2)/2));
B=fatherrand(:,ind((N-2)/2+1:end));
% 多点交叉
rnd=rand(num,(N-2)/2);
ind=rnd tmp=A(ind);
A(ind)=B(ind);
B(ind)=tmp;

% % 两点交叉
% for kk=1:(N-2)/2
% rndtmp=randint(1,1,num)+1;
% tmp=A(1:rndtmp,kk);
% A(1:rndtmp,kk)=B(1:rndtmp,kk);
% B(1:rndtmp,kk)=tmp;
% end
fatherrand=[fatherrand(:,1:2),A,B];

% 变异
rnd=rand(num,N);
ind=rnd [m,n]=size(ind);
tmp=randint(m,n,2)+1;
tmp(:,1:2)=0;
fatherrand=tmp+fatherrand;
fatherrand=mod(fatherrand,3);
% fatherrand(ind)=tmp;

%评价、选择
scoreN=scorefun(fatherrand,D);% 求得N个个体的评价函数
score(generation,:)=scoreN;
[scoreSort,scoreind]=sort(scoreN);
sumscore=cumsum(scoreSort);
sumscore=sumscore./sumscore(end);
childind(1:2)=scoreind(end-1:end);
for k=3:N
tmprnd=rand;
tmpind=tmprnd difind=[0,diff(tmpind)];
if ~any(difind)
difind(1)=1;
end
childind(k)=scoreind(logical(difind));
end
fatherrand=fatherrand(:,childind);
generation=generation+1;
end
% score
maxV=max(score,[],2);
minV=11*300-maxV;
plot(minV,'*');title('各代的目标函数值');
F4=D(:,4);
FF4=F4-fatherrand(:,1);
FF4=max(FF4,1);
D(:,5)=FF4;
save DData D

function D=code
load youhua.mat
% properties F2 and F3
F1=A(:,1);
F2=A(:,2);
F3=A(:,3);
if (max(F2)>1450)||(min(F2)<=900)
error('DATA property F2 exceed it''s range (900,1450]')
end
% get group property F1 of data, according to F2 value
F4=zeros(size(F1));
for ite=11:-1:1
index=find(F2<=900+ite*50);
F4(index)=ite;
end
D=[F1,F2,F3,F4];

function ScoreN=scorefun(fatherrand,D)
F3=D(:,3);
F4=D(:,4);
N=size(fatherrand,2);
FF4=F4*ones(1,N);
FF4rnd=FF4-fatherrand;
FF4rnd=max(FF4rnd,1);
ScoreN=ones(1,N)*300*11;
% 这里有待优化
for k=1:N
FF4k=FF4rnd(:,k);
for ite=1:11
F0index=find(FF4k==ite);
if ~isempty(F0index)
tmpMat=F3(F0index);
tmpSco=sum(tmpMat);
ScoreBin(ite)=mod(tmpSco,300);
end
end
Scorek(k)=sum(ScoreBin);
end
ScoreN=ScoreN-Scorek;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

遗传算法程序（三）：

%IAGA
function best=ga
clear
MAX_gen=200; %最大迭代步数
best.max_f=0; %当前最大的适应度
STOP_f=14.5; %停止循环的适应度
RANGE=[0 255]; %初始取值范围[0 255]
SPEEDUP_INTER=5; %进入加速迭代的间隔
advance_k=0; %优化的次数

popus=init; %初始化
for gen=1:MAX_gen
fitness=fit(popus,RANGE); %求适应度
f=fitness.f;
picked=choose(popus,fitness); %选择
popus=intercross(popus,picked); %杂交
popus=aberrance(popus,picked); %变异
if max(f)>best.max_f
advance_k=advance_k+1;
x_better(advance_k)=fitness.x;
best.max_f=max(f);
best.popus=popus;
best.x=fitness.x;
end
if mod(advance_k,SPEEDUP_INTER)==0
RANGE=minmax(x_better);

RANGE

advance=0;
end
end
return;
function popus=init%初始化
M=50;%种群个体数目
N=30;%编码长度
popus=round(rand(M,N));
return;

function fitness=fit(popus,RANGE)%求适应度
[M,N]=size(popus);
fitness=zeros(M,1);%适应度
f=zeros(M,1);%函数值
A=RANGE(1);B=RANGE(2);%初始取值范围[0 255]

for m=1:M
x=0;
for n=1:N
x=x+popus(m,n)*(2^(n-1));
end
x=x*((B-A)/(2^N))+A;
for k=1:5
f(m,1)=f(m,1)-(k*sin((k+1)*x+k));
end
end
f_std=(f-min(f))./(max(f)-min(f));%函数值标准化
fitness.f=f;fitness.f_std=f_std;fitness.x=x;
return;

function picked=choose(popus,fitness)%选择
f=fitness.f;f_std=fitness.f_std;
[M,N]=size(popus);
choose_N=3; %选择choose_N对双亲
picked=zeros(choose_N,2); %记录选择好的双亲
p=zeros(M,1); %选择概率
d_order=zeros(M,1);

%把父代个体按适应度从大到小排序
f_t=sort(f,'descend');%将适应度按降序排列
for k=1:M
x=find(f==f_t(k));%降序排列的个体序号
d_order(k)=x(1);
end
for m=1:M
popus_t(m,:)=popus(d_order(m),:);
end
popus=popus_t;
f=f_t;

p=f_std./sum(f_std); %选择概率
c_p=cumsum(p)'; %累积概率

for cn=1:choose_N
picked(cn,1)=roulette(c_p); %轮盘赌
picked(cn,2)=roulette(c_p); %轮盘赌
popus=intercross(popus,picked(cn,:));%杂交
end
popus=aberrance(popus,picked);%变异
return;

function popus=intercross(popus,picked) %杂交
[M_p,N_p]=size(picked);
[M,N]=size(popus);
for cn=1:M_p
p(1)=ceil(rand*N);%生成杂交位置
p(2)=ceil(rand*N);
p=sort(p);
t=popus(picked(cn,1),p(1):p(2));
popus(picked(cn,1),p(1):p(2))=popus(picked(cn,2),p(1):p(2));
popus(picked(cn,2),p(1):p(2))=t;
end
return;
function popus=aberrance(popus,picked) %变异
P_a=0.05;%变异概率
[M,N]=size(popus);
[M_p,N_p]=size(picked);
U=rand(1,2);

for kp=1:M_p
if U(2)>=P_a %如果大于变异概率，就不变异
continue;
end
if U(1)>=0.5
a=picked(kp,1);
else
a=picked(kp,2);
end
p(1)=ceil(rand*N);%生成变异位置
p(2)=ceil(rand*N);
if popus(a,p(1))==1%0 1变换
popus(a,p(1))=0;
else
popus(a,p(1))=1;
end
if popus(a,p(2))==1
popus(a,p(2))=0;
else
popus(a,p(2))=1;
end
end
return;

function picked=roulette(c_p) %轮盘赌
[M,N]=size(c_p);
M=max([M N]);
U=rand;
if U<c_p(1)
picked=1;
return;
end
for m=1:(M-1)
if U>c_p(m) & U<c_p(m+1)
picked=m+1;
break;
end
end

全方位的两点杂交、两点变异的改进的加速遗传算法（IAGA）
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